Page:Love, A.E.H. - A treatise on the mathematical theory of elasticity (1920).djvu/58

Rh Now, writing $$\beta$$ for $$\frac{1}{2}\pi-a$$, we have and we can observe that and that

Hence, taking axes of X and F which are obtained from those of x and y by a rotation through $$\frac{1}{4}\pi - \frac{1}{2}\alpha$$ in the sense from x towards y, we see that the particle which was at (X, Y) is moved by the pure shear followed by the rotation to the point (X2, Y2), where

Thus every plane of the material which is parallel to the plane of (X, z) slides along itself in the direction of the axis of X through a distance proportional to the distance of the plane from the plane of (X, z). The kind of strain just described is called a "simple shear," the angle α is the "angle of the shear," and 2 tan α is the "amount of the shear."